Non-parametric frequency response estimation using a local rational model1

A review of the relationship between the frequency response function of linear system and the DFT of the input and output signals show that the output DFT is a sum of two terms. The first term contain the FRF multiplied with the input DFT and the second term capture the effect when the system is not operating in a periodic fashion. The utilization of these two terms when performing non-parametric frequency response function estimation has led to the previously developed Local Polynomial Method. This paper acknowledge that the two terms can better be approximated by local rational functions with a common denominator polynomial and a new method called Local Rational Method has been developed. Numerical simulations illustrate the performance of the new rational method in comparison with the polynomial one. The results suggest that the new rational method gives better performance when the system has a resonant behavior.